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WBBSEClass 10MathematicsPythagoras Theorem05 Mark2025 Moderate

QQuestion

State and prove Pythagoras theorem.

Exam-ready answer • 05 Mark

Answer

Proof of pythagoras Theorem 2 removebg preview e1733890938299

Pythagoras Theorem: In any right-angled triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides.

Given: ABC is a right-angled triangle whose ∠A is a right angle.

To prove: BC² = AB² + AC²

Construction: I draw a perpendicular AD on the hypotenuse BC from the right angular point A which intersects the side BC at the point D.

Proof: In right-angled Δ ABC, AD is perpendicular on the hypotenuse BC.

∴ Δ ABD and Δ CBA are similar.

Hence,

{\text{AB} \over \text{BC}} = {\text{BD} \over \text{AB}},

∴ AB² = BC × BD —- (i)

Again, ΔCAD and ΔCBA are similar.

Hence,

{\text{AC} \over \text{BC}} = {\text{DC} \over \text{AC}}

∴ AC² = BC × DC —- (ii)

So, by adding (i) and (ii), I get:

AB² + AC² = BC × BD + BC × DC.

= BC (BD + DC) = BC × BC = BC².

∴ BC² = AB² + AC² [proved]

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